Details

Time bar (total: 41.9s)

sample107.0ms

Algorithm
intervals
Results
87.0ms256×body80valid

simplify207.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
206.0ms
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune43.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize80.0ms

Local error

Found 4 expressions with local error:

6.6b
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
1.0b
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
0.2b
(* (sin kx) (sin kx))
0.2b
(* (/ (* l 2) Om) (/ (* l 2) Om))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
42×add-cbrt-cube add-exp-log
22×add-sqr-sqrt
19×pow1
17×*-un-lft-identity add-cube-cbrt
16×prod-exp cbrt-unprod
12×cbrt-undiv times-frac div-exp
10×swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
3×sqrt-prod
2×pow2 pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up unswap-sqr
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ associate-*r/ fma-udef sqr-sin sin-mult
Counts
4 → 116
Calls
4 calls:
Slowest
32.0ms
(* (sin kx) (sin kx))
23.0ms
(* (/ (* l 2) Om) (/ (* l 2) Om))
5.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
0.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)

series594.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
325.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
210.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
37.0ms
(* (/ (* l 2) Om) (/ (* l 2) Om))
21.0ms
(* (sin kx) (sin kx))

simplify12.6s

Counts
96 → 128
Calls
96 calls:
Slowest
718.0ms
(* (/ (* (* (* l 2) (* l 2)) (* l 2)) (* (* Om Om) Om)) (/ (* (* (* l l) l) (* (* 2 2) 2)) (* (* Om Om) Om)))
605.0ms
(* (/ (* (* (* l l) l) (* (* 2 2) 2)) (* (* Om Om) Om)) (/ (* (* (* l 2) (* l 2)) (* l 2)) (* (* Om Om) Om)))
556.0ms
(* (/ (* (* (* l l) l) (* (* 2 2) 2)) (* (* Om Om) Om)) (* (* (/ (* l 2) Om) (/ (* l 2) Om)) (/ (* l 2) Om)))
550.0ms
(* (/ (* (* (* l 2) (* l 2)) (* l 2)) (* (* Om Om) Om)) (* (* (/ (* l 2) Om) (/ (* l 2) Om)) (/ (* l 2) Om)))
544.0ms
(* (/ (* l 2) Om) (/ (* l 2) Om))

prune2.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize85.0ms

Local error

Found 4 expressions with local error:

6.6b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
2.5b
(/ (* (sin ky) l) Om)
2.5b
(/ (* (sin ky) l) Om)
1.7b
(/ (* l (sin kx)) Om)

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
19×add-cbrt-cube add-exp-log
12×add-sqr-sqrt
11×*-un-lft-identity add-cube-cbrt
9×associate-/r* times-frac
6×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg prod-exp sqrt-prod cbrt-unprod div-inv associate-/l*
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 88
Calls
4 calls:
Slowest
28.0ms
(/ (* l (sin kx)) Om)
22.0ms
(/ (* (sin ky) l) Om)
22.0ms
(/ (* (sin ky) l) Om)
3.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))

series560.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
328.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
83.0ms
(/ (* l (sin kx)) Om)
75.0ms
(/ (* (sin ky) l) Om)
73.0ms
(/ (* (sin ky) l) Om)

simplify5.0s

Counts
55 → 100
Calls
55 calls:
Slowest
675.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
451.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
432.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
331.0ms
(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))
314.0ms
(sqrt (* (cbrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)) (cbrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))))

prune1.9s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize83.0ms

Local error

Found 4 expressions with local error:

6.6b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
2.5b
(/ (* (sin ky) l) Om)
2.5b
(/ (* (sin ky) l) Om)
1.7b
(/ (* l (sin kx)) Om)

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
19×add-cbrt-cube add-exp-log
12×add-sqr-sqrt
11×*-un-lft-identity add-cube-cbrt
9×associate-/r* times-frac
6×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg prod-exp sqrt-prod cbrt-unprod div-inv associate-/l*
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 88
Calls
4 calls:
Slowest
21.0ms
(/ (* l (sin kx)) Om)
19.0ms
(/ (* (sin ky) l) Om)
11.0ms
(/ (* (sin ky) l) Om)
1.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))

series600.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
376.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
82.0ms
(/ (* l (sin kx)) Om)
77.0ms
(/ (* (sin ky) l) Om)
64.0ms
(/ (* (sin ky) l) Om)

simplify4.6s

Counts
55 → 100
Calls
55 calls:
Slowest
432.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
411.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
368.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
315.0ms
(sqrt (* (cbrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)) (cbrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))))
292.0ms
(- (/ (* ky l) Om) (* 1/6 (/ (* (pow ky 3) l) Om)))

prune1.9s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.3b

localize80.0ms

Local error

Found 4 expressions with local error:

27.2b
(posit16->real (real->posit16 (* (/ (* l 2) Om) (/ (* l 2) Om))))
6.6b
(sqrt (fma (posit16->real (real->posit16 (* (/ (* l 2) Om) (/ (* l 2) Om)))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
1.0b
(fma (posit16->real (real->posit16 (* (/ (* l 2) Om) (/ (* l 2) Om)))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
0.2b
(* (sin kx) (sin kx))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt pow1
9×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×swap-sqr associate-*r* associate-*l* sqrt-prod
1×pow2 rem-sqrt-square sqrt-pow1 pow-plus pow1/2 pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod fma-udef sqr-sin remove-posit16 sin-mult unswap-sqr
Counts
4 → 68
Calls
4 calls:
Slowest
11.0ms
(* (sin kx) (sin kx))
1.0ms
(sqrt (fma (posit16->real (real->posit16 (* (/ (* l 2) Om) (/ (* l 2) Om)))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
0.0ms
(posit16->real (real->posit16 (* (/ (* l 2) Om) (/ (* l 2) Om))))
0.0ms
(fma (posit16->real (real->posit16 (* (/ (* l 2) Om) (/ (* l 2) Om)))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)

series557.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
308.0ms
(sqrt (fma (posit16->real (real->posit16 (* (/ (* l 2) Om) (/ (* l 2) Om)))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
180.0ms
(fma (posit16->real (real->posit16 (* (/ (* l 2) Om) (/ (* l 2) Om)))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
50.0ms
(posit16->real (real->posit16 (* (/ (* l 2) Om) (/ (* l 2) Om))))
19.0ms
(* (sin kx) (sin kx))

simplify3.6s

Counts
41 → 80
Calls
41 calls:
Slowest
503.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
414.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
404.0ms
(sqrt (sqrt (fma (posit16->real (real->posit16 (* (/ (* l 2) Om) (/ (* l 2) Om)))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
387.0ms
(sqrt (* (cbrt (fma (posit16->real (real->posit16 (* (/ (* l 2) Om) (/ (* l 2) Om)))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)) (cbrt (fma (posit16->real (real->posit16 (* (/ (* l 2) Om) (/ (* l 2) Om)))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
353.0ms
(fma (posit16->real (real->posit16 (* (/ (* l 2) Om) (/ (* l 2) Om)))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)

prune2.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.3b

regimes463.0ms

Accuracy

0% (0.1b remaining)

Error of 0.7b against oracle of 0.6b and baseline of 0.7b

bsearch6.0ms

end0.0ms

sample4.1s

Algorithm
intervals
Results
3.8s8000×body80valid